A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.

A triangular number (or triangle number) is a number that can be represented by a pattern of dots arranged into an equilateral triangle.

Problem solving with non-linear relationships

Maths

Checking understanding of arithmetic sequences

Securing understanding of arithmetic sequences

Features of geometric sequences

Recognising geometric sequences

Representing geometric sequences graphically

Features of special number sequences

Recognising special number sequences

Graphing special number sequences using technology

Extrapolating a sequence

In this unit, pupils considered geometric sequences and how they might be represented graphically. In this future unit, pupils study the graphical representation to link features of the graph to its equation.

In the sequences unit, pupils learnt how to graphically represent an arithmetic sequence. In this unit, pupils now consider geometric sequences and how these can be represented graphically.

In this unit we explore geometric and special number sequences like the Fibonacci sequence. We develop strategies to recognise types of sequence and continue them.

Non-linear relationships

This table shows the value of a car two years after it was made. If the values form a geometric sequence, what is the common multiplier between terms? (You may use your calculator.)

This table shows the value of a car 2 years after it was made. If the values continue to follow the same geometric sequence, what is the car's value after 3 years? (You may use your calculator.) £{{}}

If the geometric sequence continues the value will drop below zero pounds.

Sequences cannot go on forever, they will eventually stop.

The value of the car may stop decreasing, it could reach minimum value.

The value may decrease sharply in the first 2 years, then the pattern may change

The car loses the most value in the first year, not the same amount each year.

This table shows the value of a car two years after it was made. Why might this sequence not continue as the same geometric sequence forever?

Which two sequences can be added to make the first 5 terms of a linear sequence? 

Order these terms so they form part of a Collatz sequence: "If the term is even, the next term is half the previous term. If the term is odd, the next term is 3 times the previous term add 1".

Which two sequences can be added to make the first 5 terms of a linear sequence?

Use a calculator to work out the value of $$3^{8}$$. {{ }}.

The next term in the geometric sequence 0.4, 2, 10, ... is {{ }}.

Which of these could be the first 4 terms in an arithmetic sequence?

What is the $$n^{\text{th}}$$ term rule for the linear sequence which starts 13, 8, 3, -2, ...?

Which of these could be the first 5 terms of a sequence with a common second difference? (These are called quadratic sequences).

Problem solving with non-linear relationships

Lesson outcome